Abstract

The emissivity from a stationary random rough surface is derived by taking into account the multiple reflections and the shadowing effect.
The model is applied to the ocean surface. The geometric optics approximation is assumed to be valid, which means that the rough surface is modeled as a collection of facets reflecting locally the light in the specular direction. In particular, the emissivity with zero, single, and double reflections are analytically calculated, and each contribution is studied numerically by considering a 1D sea surface observed in the near infrared band. The model is also compared with results computed from a Monte Carlo ray-tracing method.

Illustration of the first-order illumination function. At the top (upward case),
θ1∈[0;π/2]⇒s=sgn(cos⁡θ1)=+1⁢and⁢z1≤z0. At the bottom (downward case),
θ1∈[π/2;π]⇒s=sgn(cos⁡θ1)=−1 and
z1≥z0.
zi stands for the height of the point
Mi.

(Color online) Zero-order average illumination function
S¯¯0(θ) computed from a Monte Carlo method, from Eq. (48) (without correlation) and when the correlation is taken into account versus the emission angle θ. The wind speed
u12=5m/s.

(Color online) First-order average illumination function
S¯¯1(θ) computed from a Monte Carlo method, from Eq. (50) (without correlation) and when the correlation is taken into account versus the emission angle θ. The wind speed
u12=5m/s.

(Color online) Parameters
m1(top) and
σ1(bottom) in degrees of the empirical function f versus the rms slope σs. The label “Fit” in the legend cor-responds to the linear regression of
{m1,
σ1}. The wavelengths
λ={4,
10}
μm.